In the classroom, standing in front of her blank-face students, the deaf mathematician loses her train of thought. In doing so, she thinks of this idiom, how false it is that thought follows a path like the tracks of a train. Or maybe not; train tracks split and meet again later, some tracks run parallel and never meet. And tracks end abruptly, are left unfinished or are abandoned and grown over with brush, get buried with time.

She puts her hand to her forehead to block the light and scans the room. How many of them have walked tracks at night, put toe to heel on the raised metal, felt sound coming through the ties? It is a feeling that resides in that twilight space of language somewhere between a shudder and a shake.

I’m sorry, the deaf mathematician signs and her students blink blankly. Where were we?

Three students sign back to her, Valid vs. Sound, and her thought returns to its place. She says that for an argument to be sound, it must be valid, but also, the premises must be true; if the first premise is false, then the argument is not sound.

Then she puts two premises and a conclusion on the board.

All mortals die.

I am mortal.

Therefore, I will die.

Once, one of her students objected. This was in her first year of teaching and she’d not been prepared for debate. Math, she had thought, was a discipline of fact; there was no room for belief. Things either were or were not.

If the premises must be true, the student had asked, then we have to know the first is not false. She had looked at him perplexed. How do you know all mortals die? the student asked. The room had gone still.

She had thought for a moment, wondered how to navigate this. In later years, she would be prepared, explain the divorce between theory and practice, describe the split between experiment and law. But there, a young mathematician without much experience in how to relay these ideas in writing or signs, to lovers or kids, had pulled her hands to her chest and told them she didn’t know. She told them she did not know and that it was okay, that part of math is trust.

For years she had debated whether or not she had meant it, this rule she had taught her first class. It had pacified them and they had gone on with the lesson, but often she’d spent time thinking about whether she believed it herself.

This class doesn’t object. They are clear about mortals and death.

This is both valid and sound, her most attentive student responds. They’ve started working on his application for a scholarship she’s sure he’ll receive. The deaf mathematician nods in return.

She tells them to try another and writes this on the board:

All organisms with wings can fly.

Penguins have wings.

Therefore, penguins can fly.

A student in the back whose parents just divorced explains that while the argument is valid, it is not sound, as penguins cannot fly.

She asks if they might come up with another example. A student who always sits as close to her as possible raises his hand. He has recently left home, moved in with his older brother. He is now getting better grades. The deaf mathematician calls on him by name.

All humans with ears can hear, the student signs.

Later, when she gets home, she’ll explain this scene to the photographer. Be lucky you do not teach literature, he will tell her. Be lucky you do not have to profess about a speaker, an audience, voice. Even the word language comes from the Latin for “tongue,” he will tell her. There’s just no escaping the idea that word derives from the mouth.

The deaf mathematician’s hands are wet and the chalk that cakes them is a paste. It feels like a long walk to the board. She records the premise and stays there for a moment, her back to the class, collecting herself. Then she asks, What’s next?

A girl who has never participated in class before, a girl the deaf mathematician has talked to many times in conferences about her lack of participation, raises her hand. The girl is not passive or uninterested, but nervous, she had explained, that she’d get the answer wrong.

We have ears,

the young girl says. The deaf mathematician keeps herself steady. She writes the premise slowly and clearly underneath the first. She turns around and tells her class, therefore…

The entire class signs back to her, simultaneously, the same three words.

We can hear.

The class is quiet then, taking notes and thinking to themselves, pointing to each other’s script to clarify the rule. They will take down the argument and forget it, she thinks, rolling the chalk between her fingers, the dust getting caught under her nails. She circles the room and catches a glimpse of one of her students’ notebooks.

On the margin at the top of the page, above the equation sitting on the board, the boy has written in capital letters and underlined twice:

THIS IS NOT SOUND

Lindsey Drager’s prose has appeared most recently in Web Conjunctions, Gulf Coast, West Branch Wired, Black Warrior Review, Cream City Review, Quarterly West, Kenyon Review Online, and elsewhere. A Michigan native, she is a Ph.D. candidate at the University of Denver where she edits the Denver Quarterly.